Transferring changes from UV to a mesh
You can do it manually, but it is tedious:


change the plane's 3D origin to the bottom right of the plane, so that all of the planes local coordinates are equal or above 0, like your UV coordinates

now click on each vertex of the plane and in the top part of the Proprieties panel press "Local", change Y to 0 then change X and Z to your UV coordinates

to know which vertex in UV space belongs to which vertex in 3D space , click
"Keep UV and edit mode mesh selection in sync"